Weak gravitational lensing by fourth order gravity black holes

Horváth, Zsolt and Gergely, Árpád László and Hobill, D. and Capozziello, S. and de Laurentis, M. (2013) Weak gravitational lensing by fourth order gravity black holes. PHYSICAL REVIEW D, 88 (6). ISSN 2470-0010

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Abstract

We discuss weak lensing characteristics in the gravitational field of a compact object in the low- energy approximation of fourth order f (R) gravity theory. The particular solution is characterized by a gravitational strength parameter σ and a distance scale rc much larger than the Schwarzschild radius. Above rc gravity is strengthened and as a consequence weak lensing features are modified compared to the Schwarzschild case. We find a critical impact parameter (depending upon rc) for which the behavior of the deflection angle changes. Using the Virbhadra-Ellis lens equation we improve the computation of the image positions, Einstein ring radii, magnification factors and the magnification ratio. We demonstrate that the magnification ratio as function of image separation obeys a power-law depending on the parameter σ, with a double degeneracy. No σ 6 = 0 value gives the same power as the one characterizing Schwarzschild black holes. As the magnification ratio and the image separation are the lensing quantities most conveniently determined by direct measurements, future lensing surveys will be able to constrain the parameter σ based on this prediction.

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